Benoit Cloitre

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asymptotic analysis 1 combinatorics 1 Dyck paths 1 integer sequences 1 recurrence relations 1

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math.GM2025

On a BBP-type formula for $I ¨ ^{2}$ in the golden ratio base

Benoit Cloitre

This paper presents a detailed, self-contained proof of a BBP-type formula for $I ¨ ^{2}$ expressed in the golden ratio base, $I ¨ $ . The formula was discovered empirically by the author…

math.GM2025

A study of a family of self-referential sequences

Benoit Cloitre

We introduce and analyze a three-parameter family of self-referential integer sequences $S (x, y, z)$ : starting from $a (1) = x$ , each term advances by $y$ when the index $k$ has already…

On a BBP-type formula for I¨2 in the golden ratio base

A study of a family of self-referential sequences

On a BBP-type formula for $I ¨ ^{2}$ in the golden ratio base